Some results from class: for the homogeneous linear system of differential equations there are three possibilities based on the eiganvalues for A Distinct real eigenvalues: If the matrix A has distinct real eigenvalues λ, λ2 with corresponding eigenvalues v1, V2, the general solution is Complex conjugate eigenvalues: If the matrix A has eigenvalues λ-a士 the corresponding eigen- vectors are complex and may be written as v = r,士is, with r's real. The general solution is then Repeated real eigenvalue: We did not finish this case in class, but include it here for completeness. If A is a multiple of the identity-say A-kl-then the system is just x kx and y' ky. These may be solved separately to get x-Ciekt, 3 C2ekt. If not, let λ be the unique eigenvalue. Let vo be a nonzero vector which is not an eigenvector for A and set vi = (A-λ)vo (which is an eigenvector for A). The general solution is then
